# Extraneous solutions of radical equations

Practice some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.

### Problem

Divya is solving the following equation for w.
3, w, minus, square root of, 20, minus, 5, w, end square root, equals, 2
Her first few steps are given below.
\begin{aligned} 3w&=\sqrt{20-5w}+2\\ \\ 3w-2&=\sqrt{20-5w}\\ \\ (3w-2)^2&=\left(\sqrt{20-5w}\right)^2\\ \\ 9w^2-12w+4&=20-5w \end{aligned}
Is it necessary for Divya to check her answers for extraneous solutions?
Please choose from one of the following options.